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2005 | 3 | 1 | 35-46

Article title

Nonlinear dynamics of mechanical system with external excitation


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This paper attends to the problem of vibration of a self-excited mechanical system with a relatively complicated, history dependent dry friction model. The experimentally identified friction model allows description of various cases of stationary and transient motion. The system is composed of a lumped mass that interacts with a belt by means of dry friction. The system is additionally subjected to an external harmonic excitation through elastic element. The main objective of the experimental research has been focused on the analysis of the system behaviour for various values of the excitation frequency. This paper includes also computer simulation of the vibration of the considered system and comparison between the results of experimental and theoretical analysis. The comparison enables the assumed friction model for steel-polyester pair to be verified. It was another goal of the investigations.










Physical description


1 - 3 - 2005
1 - 3 - 2005


  • Institute of Materials Science, Cracow University of Technology, Warszawska 24, 31-155, Cracow, Poland


  • [1] B. Ryczek and R. Bogacz: “Active damping of stick-slip self-excited vibration for selected external excitation frequencies”,Machine Dynamics Problems, Vol. 26, (2002), pp. 35–42.
  • [2] K. Popp, L. Panning and W. Sextro: “Vibration damping by friction forces: theory and applications”,Journal of Vibration and Control,Vol. 9, (2003),pp. 419–448. http://dx.doi.org/10.1177/107754603030780[Crossref]
  • [3] R. Bogacz, H. Irretier and J. Sikora: “On discrete modelling of contact problems with friction”,Journal of Applied Mathematics and Mechanics (ZAMM), Vol. 70, (1990), pp. 31–32.
  • [4] U. Andreaus and P. Casini: “Dynamics of friction oscillators excited by a moving base and/or driving force”,Journal of Sound and Vibration,Vol. 245, (2001),pp. 685–699. http://dx.doi.org/10.1006/jsvi.2000.3555[Crossref]
  • [5] N. Hinrichs, M. Oestreich and K. Popp: “Dynamics of oscillators with impact and friction”,Chaos, Solitions & Fractals, Vol. 8, (1997), pp. 535–558. http://dx.doi.org/10.1016/S0960-0779(96)00121-X[Crossref]
  • [6] R. Bogacz and B. Ryczek: “Dry friction self-excited vibrations; Analysis and experiment”,Engineering Transactions, Vol. 45, (1997), pp. 487–504.http://www.pk.edu.pl/~bryczek/friction1.html.
  • [7] B. Ryczek: “Quasi-harmonic vibrations in self-excited system with dry friction; Experiment and modelling”,Scientific Papers of Warsaw University of Technology, Vol. 134, (2000), pp. 99–114.
  • [8] R. Bogacz and B. Ryczek: “Modelling and analysis of frictional phenomena in dynamical systems”, In:The American Society of Mechanical Engineers (ASME) International 2001 Design Engineering Technical Conferences, Pittsburgh (USA), 2001.
  • [9] R. Bogacz and B. Ryczek: “Nonlinear vibration of mechanical systems-friction induced vibration”,Attractors, Signals and Synergetics, Vol. 1, (2002), pp. 477–496.
  • [10] R. Bogacz and B. Ryczek: “Stability analysis of frictionally excited vibrating system”,Machine Dynamics Problems, Vol. 24, (2000), pp. 21–32.

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